概率论与数理统计
mean
- 获取均值
Object mean({int dim = -1})
test
import 'package:flutter_matrix/matrix_type.dart';
main(){
data_format = "%2.5f";
var mt = Matrix.fromList([
[1, 2, 3, 1],
[2, 0, -4, double.infinity],
[0, 5, 7, -6]
]);
print(mt.mean(dim: 0));
print(mt.mean(dim: 1));
print(mt.mean(dim: 2));
}
output
[1.75, Infinity, 1.5]
[1.0, 2.3333333333333335, 2.0, Infinity]
Infinity
- 获取中位数
Object median({int dim = -1})
test
import 'package:flutter_matrix/matrix_type.dart';
main(){
data_format = "%2.5f";
var mt = Matrix.fromList([
[1, 2, 3, 1],
[2, 0, -4, double.infinity],
[0, 5, 7, -6]
]);
print(mt.median(dim: 0));
print(mt.median(dim: 1));
print(mt.median(dim: 2));
}
output
[1.5, 1.0, 2.5]
[1.0, 2.0, 3.0, 1.0]
1.5
mode
- 根据规则，在n种元素中获取众数
- 当元素个数都一样的时候返回null
- 当有t种元素个数相同的时候（t<n），取第一种元素
dynamic mode({int dim = -1})
test
import 'package:flutter_matrix/matrix_type.dart';
main(){
data_format = "%2.5f";
var mt = Matrix.fromList([
[1, 2, 3, 1],
[2, 0, -4, double.infinity],
[0, 5, 7, -6],
[1, 2, 7, -6],
[1, 1, 2, 2]
]);
print(mt.mode(dim: 0));
print(mt.mode(dim: 1));
print(mt.mode(dim: 2));
}
output
[1.0, null, null, null, null]
[1.0, 2.0, 7.0, -6.0]
1.0
shakeTotal
- 对数据进行随机抖动，范围(-bias,bias)
void shakeTotal({double bias = 1.0, int? seed})
test
import 'package:flutter_matrix/matrix_type.dart';
main(){
data_format = "%2.5f";
var mt = Matrix.fromList([
[1, 2, 3, 1],
[2, 0, -4, double.infinity],
[0, 5, 7, -6],
[1, 2, 7, -6],
[1, 1, 2, 2]
]);
mt..shakeTotal(bias: 1)..visible();
}
output
[
[ 1.12163 1.92272 3.81764 0.58426]
[ 1.56001 0.71463 -3.86042 Infinity]
[ 0.74075 4.35658 6.08286 -5.54264]
[ 1.96749 1.04282 7.97017 -6.52791]
[ 0.38011 1.53244 1.20357 2.65322]
]
shakePercent
- 对指定比例的数据进行随机抖动，范围(-bias,bias)
void shakePercent({double bias = 1.0, double percent = 0.5, int? seed})
test
import 'package:flutter_matrix/matrix_type.dart';
main(){
data_format = "%2.5f";
var mt = Matrix.fromList([
[1, 2, 3, 1],
[2, 0, 9, 7],
[0, 5, 7, -6],
[1, 2, 7, -6],
[1, 1, 2, 2]
]);
mt..shakePercent(bias: 1, percent: 0.5, seed: 0)..visible();
print(mt.count((x) => x == x.toInt(), dim: -1));
}
output
[
[ 1.00000 2.00000 3.00000 1.59552]
[ 2.00000 -0.16072 -4.00000 Infinity]
[ 0.36040 5.59324 7.00000 -6.78034]
[ 1.64683 2.62451 7.00000 -6.00000]
[ 1.00000 1.00000 1.14995 2.11472]
]
10
shakeProbably
- 对每个数据概率性随机抖动，范围(-bias,bias)
void shakeProbably({double bias = 1.0, double p = 0.5, int? seed})
test
import 'package:flutter_matrix/matrix_type.dart';
main(){
data_format = "%2.5f";
var mt = Matrix.fromList([
[1, 2, 3, 1],
[2, 0, 9, 7],
[0, 5, 7, -6],
[1, 2, 7, -6],
[1, 1, 2, 2]
]);
mt
..shakeProbably(bias: 1, p: 0.75, seed: 0)
..visible()
..shakeProbably(bias: 1, p: 0.2, seed: 0)
..visible();
}
output
[
[ 1.00000 2.00000 3.11472 1.95573]
[ 2.00000 0.62451 8.18995 7.97010]
[ 0.79149 5.74322 7.02362 -5.83102]
[ 1.00000 1.31213 6.28323 -6.08534]
[ 0.03197 0.66427 2.21624 2.00000]
]
[
[ 1.00000 2.00000 3.11472 1.95573]
[ 2.00000 0.62451 8.18995 7.97010]
[ 0.79149 5.68677 7.02362 -5.83102]
[ 1.00000 1.31213 6.28323 -6.08534]
[ 0.03197 0.66427 2.21624 2.02362]
]
shuffle
- 打乱数据
void shuffle({int? seed, int dim = -1})
test
import 'package:flutter_matrix/matrix_type.dart';
main(){
data_format = "%8.0f";
var mt = Matrix.fromList([
[1, double.nan, 3, 1],
[2, 0, 9, 7],
[0, 5, 7, -6],
[1, double.infinity, 7, -6],
[1, 1, double.negativeInfinity, 2]
]);
mt
..shuffle(dim: 0)
..visible()
..shuffle(dim: 1)
..visible()
..shuffle(dim: 2)
..visible();
}
output
[
[ 1 NaN 1 3]
[ 9 7 0 2]
[ 7 5 -6 0]
[ -6 Infinity 1 7]
[ 1 -Infinity 2 1]
]
[
[ -6 -Infinity 1 0]
[ 1 7 2 7]
[ 9 Infinity -6 2]
[ 7 5 0 3]
[ 1 NaN 1 1]
]
[
[ 1 1 2 -Infinity]
[ -6 7 0 2]
[ Infinity 5 1 7]
[ -6 1 0 1]
[ 3 9 NaN 7]
]
- 均匀分布
static T uniform<T extends MatrixBase<T>>(
{double lb = 0.0,
double ub = 1.0,
required int row,
required int column,
int? seed})
test
import 'package:flutter_matrix/matrix_type.dart';
main(){
data_format = "%2.5f";
MatrixRandom.uniform<Matrix>(row: 2, column: 8).visible();
}
output
[
[ 0.72182 0.36967 0.50301 0.59886 0.95493 0.90183 0.50644 0.13281]
[ 0.92723 0.96414 0.03060 0.92897 0.90201 0.29696 0.81846 0.58139]
]
normal
- 正态分布
static T normal<T extends MatrixBase<T>>(
{double mu = 0.0,
double sigma = 1.0,
required int row,
required int column,
int? seed})
test
import 'package:flutter_matrix/matrix_type.dart';
main(){
data_format = "%2.5f";
MatrixRandom.normal<Matrix>(row: 2, column: 8).visible();
}
output
[
[-2.11616 -2.44480 2.95000 1.16511 -1.44609 1.14767 -0.28159 -0.22208]
[-0.23525 0.78347 -0.37689 1.11326 -0.02535 0.54844 -1.11553 0.25712]
]
binomial
- 二项分布
- n是试验次数，p是成功的概率
static T binomial<T extends MatrixBase<T>>(
{required int n,
required double p,
required int row,
required int column,
int? seed})
test
import 'package:flutter_matrix/matrix_type.dart';
main(){
data_format = "%2.0f";
MatrixRandom.binomial<Matrix>(n: 10, p: 0.4, row: 2, column: 5).visible();
}
output
[
[ 5 6 4 3 4]
[ 4 1 3 4 4]
]
chisquare
- 卡方分布，其中正整数df是自由度
static T chisquare<T extends MatrixBase<T>>(
{required int df, required int row, required int column, int? seed})
test
import 'package:flutter_matrix/matrix_type.dart';
main(){
data_format = "%2.5f";
MatrixRandom.chisquare<Matrix>(df: 5, row: 2, column: 8).visible();
}
output
[
[ 2.02621 3.94982 2.45784 3.73202 4.25828 8.80980 3.70948 10.56275]
[ 3.50148 1.81609 6.09900 7.97319 7.45826 4.74143 2.30963 8.61327]
]
exponential
- 指数分布，正实数lambda是速率参数
static T exponential<T extends MatrixBase<T>>(
{required double lambda,
required int row,
required int column,
int? seed})
test
import 'package:flutter_matrix/matrix_type.dart';
main(){
data_format = "%2.5f";
MatrixRandom.exponential<Matrix>(lambda: 2.5, row: 2, column: 8).visible();
}
output
[
[ 0.08276 0.00139 0.29485 0.79533 0.12472 0.98942 0.74717 0.62893]
[ 0.61888 1.48321 0.20256 0.03876 0.70940 0.35311 0.40923 0.24835]
]
f
- F 分布。其中d1和d2是两个独立卡方分布的自由度
static T f<T extends MatrixBase<T>>(
{required int d1,
required int d2,
required int row,
required int column,
int? seed})
test
import 'package:flutter_matrix/matrix_type.dart';
main(){
data_format = "%3.5f";
MatrixRandom.f<Matrix>(d1: 1, d2: 2, row: 2, column: 8).visible();
}
output
[
[ 4.93056 0.11101 0.01529 1.57699 1.16049 0.71412 0.59531 1.83859]
[ 4.73860 0.91165 2.57683 0.11337 5.69172 0.01585 0.11492 0.44708]
]
gamma
- 伽马分布。其中k是形状参数，theta是尺度参数。它俩都是正数
static T gamma<T extends MatrixBase<T>>(
{required double k,
required double theta,
required int row,
required int column,
int? seed})
test
import 'package:flutter_matrix/matrix_type.dart';
main(){
data_format = "%3.5f";
MatrixRandom.gamma<Matrix>(k: 1, theta: 2, row: 2, column: 8).visible();
}
output
[
[ 5.14067 1.42020 1.75349 0.71228 0.01489 0.82426 0.00388 0.06545]
[ 2.22228 7.38054 0.33947 0.71414 0.19316 3.16064 0.71124 3.24876]
]
beta
- Beta分布，参数a和b分别是分子和分母的形状参数
static T beta<T extends MatrixBase<T>>(
{required double a,
required double b,
required int row,
required int column,
int? seed})
test
import 'package:flutter_matrix/matrix_type.dart';
main(){
data_format = "%3.5f";
MatrixRandom.beta<Matrix>(a: 1, b: 2, row: 2, column: 8).visible();
}
output
[
[ 0.49407 0.39837 0.09070 0.11256 0.59922 0.50666 0.15258 0.70883]
[ 0.18135 0.19389 0.18008 0.41081 0.25688 0.21515 0.07910 0.33202]
]
dirichlet
- 狄利克雷分布，alpha参数是一个长度为列且不小于2的浮点序列
- alpha 中的每个数字都必须大于0
static T dirichlet<T extends MatrixBase<T>>(
{required List<double> alpha, required int row, int? seed})
test
import 'package:flutter_matrix/matrix_type.dart';
main(){
data_format = "%3.5f";
MatrixRandom.dirichlet<Matrix>(alpha: [1, 3.3, 1.5, 0.78, 2, 2, 1.7, 2], row: 2).visible();
}
output
[
[ 0.09739 0.46528 0.03357 0.00008 0.14472 0.13976 0.08812 0.03108]
[ 0.19171 0.25310 0.14525 0.02408 0.14559 0.16670 0.03892 0.03466]
]
geometric
- 几何分布，其中p是成功的概率
static T geometric<T extends MatrixBase<T>>(
{required double p, required int row, required int column, int? seed})
test
import 'package:flutter_matrix/matrix_type.dart';
main(){
data_format = "%2.0f";
MatrixRandom.geometric<Matrix>(p: 0.25, row: 2, column: 10).visible();
}
output
[
[ 7 2 3 1 1 5 4 1 18 1]
[ 10 1 4 2 1 7 2 2 3 9]
]
gumbel
- Gumbel 分布
- 其中loc是分布众数的位置
- scale是分布的尺度参数，必须为非负值
static T gumbel<T extends MatrixBase<T>>(
{required double loc,
required double scale,
required int row,
required int column,
int? seed})
test
import 'package:flutter_matrix/matrix_type.dart';
main(){
data_format = "%2.5f";
MatrixRandom.gumbel<Matrix>(loc: 2, scale: 2, row: 2, column: 8).visible();
}
output
[
[ 0.79973 1.47329 0.77731 1.35254 1.03301 6.36100 5.02553 0.39647]
[ 2.50385 3.34456 1.25769 -0.80591 6.03160 2.28924 2.21749 1.99499]
]
hypergeometric
- 超几何分布，参数N、K、n分别表示元素总数、目标元素总数、抽取样本数，最终得到样本中目标元素的数量
static T hypergeometric<T extends MatrixBase<T>>(
{required int N,
required int K,
required int n,
required int row,
required int column,
int? seed})
test
import 'package:flutter_matrix/matrix_type.dart';
main() {
data_format = "%2.0f";
MatrixRandom.hypergeometric<Matrix>(N: 20,
K: 10,
n: 5,
row: 2,
column: 8).visible();
}
output
[
[ 0 2 2 2 2 2 2 1]
[ 3 2 1 2 4 2 3 3]
]
laplace
- 拉普拉斯分布，又称双指数分布，mu为位置参数，非负b为尺度参数。
static T laplace<T extends MatrixBase<T>>(
{required double mu,
required double b,
required int row,
required int column,
int? seed})
test
import 'package:flutter_matrix/matrix_type.dart';
main() {
data_format = "%2.5f";
MatrixRandom.laplace<Matrix>(mu: 0, b: 0.5, row: 2, column: 8).visible();
}
output
[
[ 0.62375 -0.39557 0.05964 0.69604 -0.19187 -0.31969 -0.05227 0.16362]
[ 0.00698 -1.03409 -0.06551 0.76127 2.03078 -0.47385 0.63251 0.91648]
]
logistic
- Logistic分布，其中mu和s分别是位置和尺度参数，且s大于 0
static T logistic<T extends MatrixBase<T>>(
{required double mu,
required double s,
required int row,
required int column,
int? seed})
test
import 'package:flutter_matrix/matrix_type.dart';
main() {
data_format = "%2.5f";
MatrixRandom.logistic<Matrix>(mu: 1, s: 2, row: 2, column: 8).visible();
}
output
[
[-5.19389 -5.07993 -0.57864 3.94618 -2.20507 -1.24739 1.12640 2.20015]
[ 0.49239 3.60076 3.29199 2.94326 -1.70884 4.28270 2.13897 -4.37265]
]
lognormal
- 对数正态分布，其中mu和sigma分别是位置参数和尺度参数，且sigma大于 0
static T lognormal<T extends MatrixBase<T>>(
{required double mu,
required double sigma,
required int row,
required int column,
int? seed})
test
import 'package:flutter_matrix/matrix_type.dart';
main() {
data_format = "%2.5f";
MatrixRandom.lognormal<Matrix>(mu: 2, sigma: 0.5, row: 2, column: 8).visible();
}
output
[
[18.12334 12.84363 5.79773 6.37634 4.43129 8.25890 5.64034 7.05924]
[ 9.87825 7.99804 6.27516 4.19677 11.05468 11.32761 6.01271 5.69678]
]
multinomial
- 多项分布，其中n是试验次数，p是总和为1的概率列表
static T multinomial<T extends MatrixBase<T>>(
{required int n, required List<double> p, required int row, int? seed})
test
import 'package:flutter_matrix/matrix_type.dart';
main() {
data_format = "%2.0f";
MatrixRandom.multinomial<Matrix>(n: 10, p: [0.1, 0.15, 0.05, 0.2, 0.4, 0.1], row: 2).visible();
}
output
[
[ 0 2 0 2 5 1]
[ 1 1 0 4 4 0]
]
poisson
- 泊松分布，参数lambda表示平均值
static T poisson<T extends MatrixBase<T>>(
{required double lambda,
required int row,
required int column,
int? seed})
test
import 'package:flutter_matrix/matrix_type.dart';
main() {
data_format = "%2.0f";
MatrixRandom.poisson<Matrix>(lambda: 2, row: 2, column: 8).visible();
}
output
[
[ 4 2 5 0 3 4 1 1]
[ 3 1 0 3 2 3 5 0]
]
cauchy
- 柯西分布，参数x0表示中心位置，正数gamma表示尺度
static T cauchy<T extends MatrixBase<T>>(
{required double x0,
required double gamma,
required int row,
required int column,
int? seed})
test
import 'package:flutter_matrix/matrix_type.dart';
main() {
data_format = "%2.5f";
MatrixRandom.cauchy<Matrix>(x0: 0, gamma: 1, row: 2, column: 8).visible();
}
output
[
[-36.62911 0.72481 3.37703 1.14735 0.12744 -0.28093 -5.73963 0.85222]
[ 2.07105 1.33930 -0.90362 -0.71522 -4.79772 3.65556 -0.45629 -0.69549]
]
pareto
- 帕累托分布，正数xm是尺度参数，正数alpha是形状参数
static T pareto<T extends MatrixBase<T>>(
{required double xm,
required double alpha,
required int row,
required int column,
int? seed})
test
import 'package:flutter_matrix/matrix_type.dart';
main() {
data_format = "%2.5f";
MatrixRandom.pareto<Matrix>(xm: 1, alpha: 1, row: 2, column: 8).visible();
}
output
[
[ 2.13617 1.05138 2.59410 1.69382 2.13383 7.34943 1.93597 1.61736]
[ 1.35915 1.16898 4.63186 4.15207 1.76849 14.69354 2.31302 2.73154]
]
rayleigh
- 瑞利分布，正数sigma是尺度参数。
static T rayleigh<T extends MatrixBase<T>>(
{required double sigma,
required int row,
required int column,
int? seed})
test
import 'package:flutter_matrix/matrix_type.dart';
main() {
data_format = "%2.5f";
MatrixRandom.rayleigh<Matrix>(sigma: 1, row: 2, column: 8).visible();
}
output
[
[ 1.07546 2.06677 1.11999 0.53733 1.10249 1.15054 2.22445 1.53285]
[ 0.77856 1.41063 0.24988 2.02035 1.24209 1.57036 1.73024 2.23977]
]
triangular
- 三角分布，下限a，上限b，众数c。
static T triangular<T extends MatrixBase<T>>(
{required double a,
required double b,
required double c,
required int row,
required int column,
int? seed})
test
import 'package:flutter_matrix/matrix_type.dart';
main() {
data_format = "%2.5f";
MatrixRandom.triangular<Matrix>(a: -2, b: 3, c: 0, row: 2, column: 9).visible();
}
output
[
[ 0.71009 -0.91656 0.16837 -1.15603 1.52162 0.94240 0.88847 0.36057 0.14813]
[ 1.97316 -0.85960 0.44336 -0.01748 0.50504 2.18705 -0.69879 -0.07549 -0.01691]
]
wald
- 逆高斯分布（也称为 Wald 分布），均值为正数mu，形状参数为lambda
static T wald<T extends MatrixBase<T>>(
{required double mu,
required double lambda,
required int row,
required int column,
int? seed})
test
import 'package:flutter_matrix/matrix_type.dart';
main() {
data_format = "%2.5f";
MatrixRandom.wald<Matrix>(mu: 1, lambda: 2, row: 2, column: 9).visible();
}
output
[
[ 0.81247 0.62909 0.45730 3.96918 1.60884 0.48366 2.83001 1.14535 0.35252]
[ 0.59226 0.86075 1.60548 0.96771 0.46557 0.68437 0.45168 1.52735 0.64942]
]
weibull
- 威布尔分布，尺度参数lambda和形状参数k均为正数
static T weibull<T extends MatrixBase<T>>(
{required double k,
required double lambda,
required int row,
required int column,
int? seed})
test
import 'package:flutter_matrix/matrix_type.dart';
main() {
data_format = "%2.5f";
MatrixRandom.weibull<Matrix>(k: 1, lambda: 2, row: 2, column: 8).visible();
}
output
[
[ 1.77253 2.04454 0.79726 0.03651 0.41815 1.14795 0.26157 0.63567]
[ 1.26025 0.62709 2.27595 0.50974 0.14316 2.67833 0.65225 1.38974]
]
vonmises
- 冯·米塞斯分布，参数mu和k分别表示位置和浓度，k > 0
static T vonmises<T extends MatrixBase<T>>(
{required double k,
required double mu,
required int row,
required int column,
int? seed})
test
import 'package:flutter_matrix/matrix_type.dart';
main() {
data_format = "%2.5f";
MatrixRandom.vonmises<Matrix>(k: 1, mu: 2, row: 2, column: 8).visible();
}
output
[
[ 0.21612 2.38583 2.33520 2.44294 0.70750 1.90340 2.35548 1.59108]
[ 3.54407 2.16340 1.06748 3.17789 0.73116 1.55998 3.85376 1.58202]
]
t
- 学生 t 分布，正整数 v表示自由度，mu是非中心参数。
static T t<T extends MatrixBase<T>>(
{required int v,
required double mu,
required int row,
required int column,
int? seed})
test
import 'package:flutter_matrix/matrix_type.dart';
main() {
data_format = "%2.5f";
MatrixRandom.t<Matrix>(v: 5, mu: 1, row: 2, column: 8).visible();
}
output
[
[ 0.62758 2.62640 2.62945 1.69008 -2.20297 -0.34357 2.35201 0.05813]
[ 0.77000 0.98190 4.40171 1.47281 2.35428 0.31133 2.76713 1.65198]
]
frechet
- Fréchet分布，也称为逆威布尔分布，正数alpha是形状参数，比例参数s也是正数，m是位置参数
static T frechet<T extends MatrixBase<T>>(
{required double alpha,
double s = 1.0,
double m = 0.0,
required int row,
required int column,
int? seed})
test
import 'package:flutter_matrix/matrix_type.dart';
main() {
data_format = "%2.5f";
MatrixRandom.frechet<Matrix>(alpha: 1, row: 2, column: 8).visible();
}
output
[
[ 1.03756 0.66498 6.86990 0.72205 1.37044 83.75532 0.82821 0.91106]
[ 0.80854 2.80326 0.72205 2.69117 6.89905 0.71063 2.93813 2.07763]
]
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